Relative Identity in Heidegger

Poor neglected blog; even my images are dead now. Ah well, mourning is for the dead.

I have noted before that Heidegger had read some Frege; this isn't a huge surprise, given that he was a student of Husserl, but it's easy to forget from our current "analytic/continental" vantage point. I just stumbled across a place that reminded me of this, and where better to make a note of it than on a dead blog?

In section 44 of "Being and Time", Heidegger is concerned with picking apart the view of truth as adequatio intellectus et rei. His point in doing this isn't to deny the view so much as to complain that it obscures what is significant about truth: if we try to have a "thing" and a "mind" already in view, and then want to add "truth" (and falsity) on top of those as a certain kind of relation between the two ("agreement", "correspondence", or the lack of this), then we have gone badly awry: instead we need to first have Dasein's openness to the world in view, and then the "mind" and "thing" which are supposed to "agree" will all show up as abstractions from a more important phenomena which originally makes claiming possible at all.

One of the ways Heidegger tries to do this is by poking at the "adequatio" relation, which Heidegger translates as "Übereinstimmung": "Was meint überhaupt der Terminus »Übereinstimmung«?", what does one in general mean by the term "agreement"? It has to be some sort of relation, it has to be a bringing-together of two things, but clearly not just any relation will do: we need to get a sort of "agreement" which relates a "thought" and a "thing" just in that the one agrees with the other with regards to truth: and this is obscure. Plausibly, the only way to pick out the right sort of relation is by already having an understanding of truth: A true thought agrees with its object just in that the thought says that things are thus-and-so with the object, and the object is thus-and-so -- and cashing out this "says that" talk already will involve a notion of truth, for saying that things are thus-and-so is just to put forward "things are thus-and-so" as true. (And so adequatio intellectus et rei is empty as a definition of truth; it moves in a circle.)

But that is not what interests me -- I want instead to point to a moment in Heidegger's discussion of relations of "agreement":

Die Zahl 6 stimmt überein mit 16 - 10. Die Zahlen stimmen überein, sie sind gleich im Hinblick auf das Wieviel. Gleichheit ist eine Weise der Übereinstimmung. Zu dieser gehört strukturmäßig so etwas wie ein »Hinblick auf«. Was ist das, im Hinblick worauf das in der adaequatio Bezogene übereinstimmt?

Auf Englisch: The number '6' agrees with "16-10". The numbers agree, they are equal in regard to "how many". Equality is one way of agreeing. To this belongs structurally something like a "regards to". What is that in regards to which the terms related by "adequatio" agree? [This is my own translation; someone please let me know if I've fouled it up too much.]

Heidegger here mentions numerical equality as one form of "agreement", and says that "agreement" always takes a complement: Two things agree in some particular respect, with regards to something: For example, '6' and "16-10" agree in coming to the same number, but not in being the same arithmetical formula.

Heidegger here puts forward (as unproblematic and not in need of argument) a view of equality as distinct from identity; equality is only sameness of number, not "sameness" as such. This is Frege's early view, in Begriffschrift; I believe he changes to his more familiar view (that equality simply is identity) in "Sense and Reference", when he settles on truth-values as the referents of sentences -- that move lets him consolidate a fair bit of his notation. (I would check this if I were not too lazy to do so.)

More interestingly (if you are me), Heidegger also puts forward as unproblematic a view of the genus of which numerical equality is a species, a view of what I think we analytics usually call "identity", as needing a complement: "Wieviel", "How much?" specifies the sense in which '6' and "16-10" are identical, they are the same number. Without some such question as this, no species of "agreement" is specified: The question "Do they agree, are they identical?" does not itself have a sense, unless the context makes clear in what respect agreement is being asked about. (It may be that the context makes clear that every respect is meant, and any dissimilarity will be an absolute lack of agreement between the one and the other.)

If I am reading Heidegger correctly here, then he agrees with Geach against Frege (and against the vast majority of analytic philosophers) in holding that "identity is relative": that to say that A and B are identical is, in the primary case, to say that they are the same in some definite respect, such as being the same color or the same make of shoe. To say that they are absolutely identical, which Frege had taken as the more primordial notion, Geach claims is only to say that they are the same in every respect: they are the same color, the same make of shoe, occupy the same location in space, etc. -- Geach uses Leibniz's Law to introduce the notion of "absolute" or "simple" identity as a defined term in logic.

To remind the reader of the opposing view: Many have held that to say that A and B are the same color is, when put in a logically regimented way, to say that

There is an X and a Y such that X is the color of A, and Y is the color of B, and that X is (absolutely) identical to Y, and that there is no Z such that Z is the color of A or Z is the color of B and Z is not (absolutely) identical to X (and to Y).

This way of rewriting "A is the same color as B" carries with it an ontological commitment to colors; Quine and Davidson take this commitment along happily (Davidson a little more happily than Quine), and so see a sort of Platonism as an unexciting logical consequence of some ordinary claims: There are colors, and there are shapes, because there are true claims on the order of "X and Y are the same shape", and writing those out in a logically acceptable way involves committing oneself to the truth of "There is a W such that W is a shape".

Geach is able to avoid these commitments: he treats "A is the same color as B" as a primitive equivalence relation in the language, and so does not need to quantify over colors to write "A is the same color as B" in ordinary first-order logical notation; it just comes out as looking like "aRb". By a neat trick, Geach notes that he can (in a sense) keep his ideology conservative as well: Quine's way of writing "A is the same color as B" requires a way to say "A has a color", which he writes as "There is an X such that X is the color of A"; Geach writes "A has a color" as "A has the same color as A", as anything which lacks a color cannot be the same color as anything: he is able to use his primitive equivalence relations to do the work of coloredness-predicates, and so doesn't need the latter as primitive terms in his language. This trick works in general for turning predicates into equivalence relations. So Geach doesn't need to include more predicates in his language than Quine did, but is able to reduce his ontological commitments. And since Geach is able to introduce a sign for "absolute" identity in his language by means of Leibniz's Law, the resulting calculus is just Quine's beloved first-order predicate calculus with identity; Geach disagrees with Quine not over a matter of regimented logical notation, but of how to rewrite ordinary language claims in that regimented form.

There are a few other wrinkles to Geach's account of relative identity, but hopefully the above is clear enough to get it in view. One aspect of his view which Geach finds remarkable is that he, unlike Frege, is able to treat statements of sameness and statements of number along the same lines: where Frege insisted that "How many?" required a complement, that statements of number were assertions about concepts, he had also insisted that "Are A and B identical?" required no complement, and that this identity was a logically peculiar notion which everyone immediately grasps in a special way. Geach thinks this was quite odd of Frege; Frege had demolished the idea that "oneness" is a special property of every object, and had left "self-identity" as a special property of every object: but in English and German both we have the phrase "one and the same" "ein und dasselbe", which Geach thinks should have already suggested to Frege that sameness and oneness ought to be handled along the same lines. I think that Heidegger had (without having much affection for logical notation) done just this: he requires an im Hinblick auf before questions of sameness are answerable. It would be interesting to see if Heidegger was consistent in this; rejecting "absolute" in favor of "relative" identity has a fair number of consequences in metaphysics, as Geach was well aware -- puzzles about whether a statue is identical with its clay fall to the ground, for example -- and Heidegger is not uninterested in a number of these metaphysical puzzles.

Geach's "Mental Acts" and the dualism of the conceptual and the sensible

I have been reading through "Mental Acts" over the past few days. It's long been on my short list of things to read, but I'd never picked the book up until this week. (Literally: if I had seen for myself how short it was, I would've gotten it read years ago.)

It's mainly good, in the way that everything I've read by Geach has been mainly good.

I am making a post about it largely as a reminder to myself: Chapter 15, "Judgements About Sensible Particulars [Reference to Particulars]" is striking, from a Kantian perspective. But spelling out what I find so striking about it is probably of more general interest.

Geach's puzzle is about how we can judge about particulars, given that judgements are acts of our conceptual capacities, and our conceptual capacities are always universal (as they are capable of repeated use independently of what might be presently sensed).

The judgement he considers is "That flash was before this bang", uttered on different occasions and referring to different flashes and bangs. Of this he says "there is no difference to be found on the side of the judgement itself [on these two occasions]. What we may call the intelligible content of the judgement is the same in all judgements expressible as "that flash was before this bang", regardless of which flash and bang are in question." (ps.63-64) So, given that judgements are always capable of being formed regardless of occasion, how can any judgement have reference to an occasion?

Geach's answer: "How could the utterance "flash before bang" be taken to refer to a particular flash and bang? The answer is obvious[!]; the utterance can be, and probably will be, so understood in a sensory context in which the hearer notices a flash and a bang. Similarly, the utterance "some cats, white" could be taken to refer to particular cats if its hearer was looking attentively in the right direction. The content of the judgement is always intelligible and conceptual -- acquaintance with a particular sensible thing is no part of the judgement itself -- but an act of judgement performed in a particular sensory context may thereby be referred to particular sensible things." (p.64)

The most striking fact about this answer is that Geach tries to answer the question of how judgement can have reference to particulars by referring to what a hearer would take an utterance to refer to, in a given context. He seems to want to answer the question of how thought can be about the world by noting that others take it to be so: but this is patently Munchhausenianism, with empirical content being pulled up by its own bootstraps. Unless the hearer can already judge concerning particulars, then she can't take an utterance to refer to particulars: so it does no good for Geach to appeal to her judgements on the matter.

But this may be unfair: he seems to not notice what he has said, and thinks of all the work in his picture as being done by "the context" of a judgement. How to spell this out, he is unsure of: "It is clear, indeed, that the act of judgement must bear a closer relation than mere simultaneity to the context of sense-perception that gives it its special reference to these particular sensible things; I am not prepared to characterize this special relation it must bear to its context.... But I do not think this throws any doubt on what I have said; although more remains to be said." (p.64)

It is "clear" to Geach that context must be able to do this work, for we do in fact judge about particulars, and he doesn't see anything else that can make inherently-universal judgements latch onto sensible things. He is aware that "mere" simultaneity between an act of judgement and a thing will not suffice, but I hear in this the suggestion that something more than "mere" simultaneity will do the work: Judgement + Thing + Simultaneity + Y = Judgement is about Thing; future philosophy can solve for Y.

I begin here a long aside:

I find this sort of buck-passing in philosophy disagreeable, setting aside the particular problem Geach lays out for working on: it is too easy for everyone to only think through a problem so far, because "others" can always do the rest of the work. I encountered a particular egregious version of this in a seminar recently: several rival positions on a topic in the metaphysics of social groups were compared, and a criticism against one of them (I believe it was Searle's) was rejected on the grounds that if it worked, it would work for all of the positions on offer: "And if it's everybody's problem, then it's also nobody's problem", it was said with a grin. This sort of "metaphysics" struck me as nothing but intellectual masturbation: it was an intentionally restricted way of thinking, and could never bear fruit. The sort of thing people made fun of scholasticism for.

Immediately after the last Geach quote, he continues: "The problem I have just been discussing -- how we judge about sensible particulars -- was much agitated in the Middle Ages; and in my solution of it I believe I am following Aquinas. Aquinas's expression for the relation of the 'intellectual' act of judgement to the context of sense-perception that gives it a particular reference was "conversio ad phantasmata", "turning round towards the sense-appearances". [I don't know why Geach gives a gloss on this; the book is peppered with untranslated Latin phrases.] This metaphorical term is obviously a mere label, with negligible explanatory value;  but it does not pretend to be more than a label. Aquinas has, in my opinion, at least rightly located the problem; the problem is not how we advance from judgements like this is before that to more general judgements, but contrariwise how a judgement inherently general can be tied down to referring to particular things (Ia q. 86 art. 1)" (p.65)

What do we find, if we follow Geach's pointer to Thomas? Here we read that "Our intellect cannot know the singular in material things directly and primarily.... But indirectly, and as it were by a kind of reflection, it can know the singular, because, as we have said above (Question 85, Article 7), even after abstracting the intelligible species, the intellect, in order to understand, needs to turn to the phantasms in which it understands the species, as is said De Anima iii, 7. Therefore it understands the universal directly through the intelligible species, and indirectly the singular represented by the phantasm."

So in the passage Geach cites, Thomas points a few pages earlier in his book. I believe there is an error in the online edition here; Question 85, Article 7 seems irrelevant, but Question 84, Article 7 is about precisely this question: "Whether the intellect can actually understand through the intelligible species of which it is possessed, without turning to the phantasms?" Thomas's sed contra is that "The Philosopher says (De Anima iii, 7) that "the soul understands nothing without a phantasm."" -- so even in following Geach's pointer to Aquinas through Aquina's pointer to Aquinas through an incorrect citation to Aquinas we find: a pointer to Aristotle. (In fairness to Aquinas, he had given the same reference in the first place Geach pointed to.)

But Thomas does add some argumentation in support of Aristotle's view, in his replies in the same article. He states the view he is defending thusly: "In the present state of life in which the soul is united to a passible body, it is impossible for our intellect to understand anything actually, except by turning to the phantasms." -- But now it emerges that Thomism cannot help Geach here, for Thomas is concerned with a narrower problem than the one Geach has. Geach needs an answer for how judgement can be about particulars, but Thomas is concerned only with how our, human, intellect has need of "turning to the phantasms". So in his replies, he appeals to psychological facts about our minds (even appealing that "anyone can experience this of himself") to ground the need for "turning to the phantasms". But Geach's problem is a logical one: how can it be so much as possible that "inherently general" judgements can be "tied down to referring to particular things?" It is no help to note that, in fact, our judgements are so tied down, and human minds cannot but be so tied down: Thomas's investigations enter too late to be of use.


(I won't trouble with looking at De Anima III 7; I remember the passage in question, and looking at it will not help make Geach's puzzle clearer. From what I could see, Aristotle was merely marking a psychological fact with his "no thought without an image" remark: there are always things fluttering about "before the eye of the mind" while we think. But merely noting this does not make thinking less mysterious.)

I end here my long aside.


--So, Geach thinks he can tell that there must be a Y such that Judgement + Thing + Simultaneity + Y = Judgement is about Thing.

Geach faces the same problem in his next chapter, "Judgements Involving Identifications [Judgements of Identification]", which involves judgements that contain proper names. It appeared that perhaps "This flash" could be made to pick out the right flash by demonstrative ostension; proper names do not appear handleable this way, as "Smith" can be Smith's name even if Smith is not within my ostensible reach. Geach closes out his discussion of this problem with a simile: "The problem how you call Smith, the right Smith, to mind is like the problem how you call him ([Philosophical Investigations], Part I, ss691). Although lots of people are called "Smith", the summons "Smith!" may be quite effective to fetch the Smith I want if he is the only man of that name within earshot; and similarly, a judgement that might in principle relate to many men may yet in a particular real-life context be relatable to just one." (p. 73)

Here again we see the pattern of
1. There is a problem for my view of judgement.
2. In "real-life" this problem does not arise.
.'. 3. Context must supply what is lacking in my view.

At no point does Geach consider that our conceptual capacities might inherently refer to particulars, just as he knows they are inherently general. He sees that empiricism asks a bad question when it tries to solve hour we can judge of general matters, given that we can judge of particular ones; but he thinks their error was that the real question is how we can judge of particular matters, given that we can judge of general ones. There is a dualism of the conceptual and the sensible in Geach, just as there is in the empiricists he spends so much time attacking. And if he is right about the medievals, Thomas errs on his side while many Thomists and other scholastics err with the empiricists, with Aristotle claimed by all parties. If nothing else, reading Geach has been good for helping me see that Kant's problems are not new -- or at least they can be seen to have caused trouble, beneath the surface, further back than Kant traces his histories.

On a final note (and this was actually what I originally found interesting enough to post on, before I got caught up in providing context for it), Geach notes that "Quite similar considerations apply to judgements involving tense. The difference between judgements to the effect that a hydrogen bomb will be exploded and that a hydrogen bomb has been exploded is an intelligible or conceptual difference -- a specifically different exercise of concepts is involved. But there is no conceptual difference between judgements formed in different years to the effect that a hydrogen bomb has been exploded, although such a judgement formed in 1940 would have been false and one formed in 1956 would be true." (p.65) When I first read it, I was surprised by how closely connected Geach's claim about tense was to his claims about judgements of particulars: they are treated of in the same section, are said to have "similar considerations" applying to them, and I thought that perhaps the same Kantian solution was what he had overlooked. I had hopes that perhaps here I could finally find a compelling argument for why time is the form of all intuition, what the connection is between reference to particulars and reference to temporal entities. But thinking on it more, I think Geach is just mistaken about how tenses work in language (in thought): it is the same conceptual capacity at work when I judged yesterday that I would be up all night and when I judge today that I was up all night; what has changed is not the judgement, but the context in which it is considered. There is an indexical element to judgements involving tense, just as with judgements involving the concept "now", and changes of index are not changes of indexical. (Ironically, I take this to be something I learned from reading Anscombe on the first person.)

But if this is where Geach went wrong, then the connection between reference to particulars and time boils down to the connection between reference to particulars and the indexicals "here" and "now". And it strikes me as hopeless to try to establish why space and time must be forms of intuition from the fact that (as it happens) we have spatial and temporal indexicals in our language; for if there are other possible forms of intuition, presumably the minds which intuit by them have their own indexicals. So again Kant is proving damnably right: I cannot show why space and time are (our, the) forms of intuition, though it seems clear that they are. So for now I am no better than Geach; I daydream about "others" solving that problem, and think it must have a solution!